Blender Vertices Merge Problem
He is definitely doing it right in the tutorial so the problem lies somewhere in the part you have not revealed any information about - in something that you did differently. The thing to do here would be to redo it all again until it works carefully tracking and keeping all your actions in mind. This is how tutorials should usually be approached.
I guess, you may have double geometry and when you select the vertices, some overlapping vertices remain unselected. You could try to redo the whole part from start or select all and merge vertices by distance first.